The microfluidic passive control of microparticles largely relies on the hydrodynamic effects of the carrier media such as Newtonian fluids and viscoelastic fluids. Yet the viscoelastic/Newtonian interfacial effect has been scarcely investigated, especially for high-resolution particle separation. Here we report a microfluidic co-flow of Newtonian (water or PBS) and viscoelastic fluids (PEO) for the size-dependent separation of microparticles. The co-flow condition generates a stable viscoelastic/Newtonian interface, giving rise to the wall-directed elastic lift forces that compete with the center-directed lift forces, and efficiently hinders the migration of microparticles from the Newtonian to the viscoelastic fluid in a size-dependent manner. An almost complete separation of a binary mixture of 1 mu m and 2 mu m polystyrene particles is achieved by the co-flow of water and a very dilute PEO solution (100 ppm), whereas the sole use of water or PEO could not lead to an efficient separation. This co-flow microfluidic system is also applied for the separation of Staphylococcus aureus (1 mu m) from platelets (2-3 mu m) with > 90% efficiencies and purities.